An explicit estimate of the Bergman kernel for positive line bundles

TL;DR

This paper provides an explicit lower bound estimate for the Bergman kernel associated with positive line bundles, offering a concrete version of Tian's partial $C^0$-estimate in the context of compact Riemann surfaces.

Contribution

It introduces an explicit lower bound estimate for the Bergman kernel, enhancing understanding of its behavior for positive line bundles.

Findings

Explicit lower bound for Bergman kernel established

Connection to Tian's partial $C^0$-estimate clarified

Applicable to compact Riemann surfaces

Abstract

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian's partial $C^0$-estimate.